Medical examination of the human body by touch, called palpation, reveals external abnormalities that may instigate additional investigation. In breast exams or prostate exams, clinicians use palpation to detect abnormal stiffness, which may point to diseased or cancerous bodily structures. Scientists have measured changes in the stiffness of biological structures by measuring their elasticity moduli ex vivo. For example, scientists have found that infiltrating ductile carcinomas are much stiffer than any other breast tissues, and prostate cancers are stiffer than normal prostate tissues. Stiff tissue has a high elasticity modulus and shows less strain under applied force than soft tissue. Thus, by applying compression and estimating the strain, stiffness in bodily structures can be obtained.
An early medical application of ultrasound imaging included the monitoring of blood flow by the use of the displacement technique. Strain can be computed from a derivative of the displacement. With this understanding, conventional elasticity imaging is based on estimating displacements from echoed ultrasound signals to calculate strain in bodily structures. However, conventional elasticity imaging suffers from both image quality and computational burden, which have prevented successful commercialization of the technology for clinicians to use. Because of the domination of the displacement technique, many attempts at improving the calculation of strain have focused on measuring displacement ever more accurately.
In medical ultrasound, strain in an object can be estimated using ultrasound echo signals acquired before and after object compression. Strain represents the amount of deformation and is defined as:
                              Δ          ⁢                                          ⁢          L                L                            (        1        )            where L is the length of an object and ΔL is the amount of change in the object length under uni-axial force. Conventional ultrasonic strain estimation methods are based on estimating displacements between ultrasound signals acquired before and after compression. Once displacements are estimated, strain is computed from a spatial derivative of the displacement as follows:
                                          d            2                    -                      d            1                          L                            (        2        )            where d1 and d2 are the displacements at two different locations and L is the distance between these two locations (defined as the strain sample length).
For conventional strain estimation, displacements can be very large (e.g., more than a hundred micrometer), whereas the displacement difference converted to strain is very small (e.g., few micrometers). Consequently, if the strain were computed from large displacements, a tiny error in displacement estimation could magnify the error in the computation of the strain. Because strain constitutes such a small part of the displacement, scientists have resorted to displacement interpolation techniques to find the strain. To obtain desired results, hundreds of points may need to be interpolated, resulting in onerous computational effort, hindering production of marketable machinery.